# Isolated singularities of mappings with the inverse Poletsky inequality

### Abstract

The manuscript is devoted to the study of mappings

with finite distortion, which have been actively studied recently.

We consider mappings satisfying the inverse Poletsky inequality,

which can have branch points. Note that mappings with the reverse

Poletsky inequality include the classes of con\-for\-mal,

quasiconformal, and quasiregular mappings. The subject of this

article is the question of removability an isolated singularity of a

mapping. The main result is as follows. Suppose that $f$ is an open

discrete mapping between domains of a Euclidean $n$-dimensional

space satisfying the inverse Poletsky inequality with some

integrable majorant $Q.$ If the cluster set of $f$ at some isolated

boundary point $x_0$ is a subset of the boundary of the image of the

domain, and, in addition, the function $Q$ is integrable, then $f$

has a continuous extension to $x_0.$ Moreover, if $f$ is finite at

$x_0,$ then $f$ is logarithmic H\"{o}lder continuous at $x_0$ with

the exponent $1/n.$

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